What is the integral of 2/(e^{2x)-1} ?

The integral of 2/(e^{2x)-1} is ln|e^{2x}-1|-2x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2/(e^{2x)-1}

\int \frac{2}{e ^{2 x} - 1} d x

ln e^{2 x} - 1 - 2 x + C

Solution steps

\int \frac{2}{e ^{2 x} - 1} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int \frac{1}{e ^{2 x} - 1} d x

\frac{1}{e ^{2 x} - 1} = \frac{e ^{2 x}}{e ^{2 x} - 1} - 1

= 2 \cdot \int \frac{e ^{2 x}}{e ^{2 x} - 1} - 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 2 (\int \frac{e ^{2 x}}{e ^{2 x} - 1} d x - \int 1 d x)

\int \frac{e ^{2 x}}{e ^{2 x} - 1} d x = \frac{1}{2} ln e^{2 x} - 1

\int 1 d x = x

= 2 (\frac{1}{2} ln e^{2 x} - 1 - x)

Simplify

2 (\frac{1}{2} ln e^{2 x} - 1 - x) : ln e^{2 x} - 1 - 2 x

= ln e^{2 x} - 1 - 2 x

Add a constant to the solution

= ln e^{2 x} - 1 - 2 x + C

\int \frac{x}{64 - x ^{2}} d x

\int \frac{7 x ^{3} - 8 x}{x} d x

\int 8 x^{- 1} + 6 d x

\int csc^{4} (8 t) cot (8 t) d t

\int x^{2} \cdot csch (x^{3} + 1) d x

What is the integral of 2/(e^{2x)-1} ?
The integral of 2/(e^{2x)-1} is ln|e^{2x}-1|-2x+C